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Cost optimal control of Piecewise Deterministic Markov Processes under partial observation

Lange, Dirk Klaus

Abstract:
This work deals with the optimal control problem for Piecewise Deterministic Markov Processes (PDMP) under Partial Observation (PO).

The total expected discounted cost over lifetime shall be minimized while neither the states of the PDMP nor the current or cumulated cost are observable. Only noisy measurements (with known noise distribution) of the post-jump states are observable. The cost function, however, depends on the trajectory of the unobservable PDMP as well as on the observable noisy measurements of the post-jump states.

Admissible control strategies are history dependent relaxed piecewise open loop strategies: For each point in time and depending on the observable history up to this time, a probability distribution on the action space is selected. This probability distribution defines an expected control action on the jump rate, the drift and the transition kernel at jump times of the PDMP.

We first transform the initial continuous-time optimization problem under PO into an equivalent discrete-time optimization problem under PO. For the latter one, we obtain a recursive formulation for the filter: the probabilit ... mehr


Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Hochschulschrift
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000069448
URN: urn:nbn:de:swb:90-694487
KITopen ID: 1000069448
Verlag Karlsruhe
Umfang VIII, 158 S.
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Stochastik (STOCH)
Prüfungsdatum 15.02.2017
Referent/Betreuer Prof. N. Bäuerle
Schlagworte Piecewise Deterministic Markov Process, Partial Observation, Stochastic Dynamic Programming, Optimal Policy, Young Topology
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